One leg of a right triangle is 3 millimeters longer than the shorter leg, and the hypotenuse is 6 millimeters longer than the shorter leg. Find the lengths of each side of the triangle.

Question

anonymous · Answer

@animal_lover36 @Abbygirl15 @Artsy_Brian @agbyoung @Agl202 @aaronq

agl202 · Answer

x will be the length of the short side. Using the Pythagorean Theorem: 

x^2 + (x + 3)^2 = (x + 6)^2 

2x^2 + 6x + 9 = x^2 + 12x + 36 
x^2 = 6x + 27 
x^2 - 6x - 27 = 0 
(x + 3)(x - 9) = 0 
x = -3 or x = 9 

Since length typically isn't negative: 

x = 9 

So, side one is 9, side 2 is 12, and side 3 is 15 

To verify: 
9^2 + 12^2 = 15^2 
81 + 144 = 225

anonymous · Answer

Ok thank you so much!!!!!!!!

anonymous · Answer

Hey @Agl202 could you please help me with another one that is similar?

anonymous · Answer

are you there @Agl202